Why I hate formula triangles

For one of my PGCE interviews, I was told to prepare a lesson plan for a physics lesson (which made sense since I was applying to the PGCE Physics with Maths). I figured I’d link the two, and do a lesson on speed-distance-time calculations. I remember at school some people using formula triangles (often misnamed ‘equation triangles’) so figured they’d be a good way to scaffold the work for anyone that struggled. Of course, I wasn’t ever going to teach this lesson, but they wanted to see what my thinking was like I guess.

They ripped me to shreds. “Formula triangles are awful and we don’t approve of their use.” No real qualification as to why. I’d never really thought about it in any detail, but this seemed harsh. And besides, at that point I’d had literally no training to teach, so how would I know they’d hate it so much? (As a side, they also told me I didn’t have enough school experience from my one-day-per-week for several months at university… Needless to say I didn’t accept their offer)

I forgot about the whole debacle for a bit and used them briefly as an NQT, but then at some point I saw a tweet I think about how they teach bad habits, and I thought about it, and loosely agreed. During the period where I was using them, the second I introduced a new formula I would instantly be met with “what’s the triangle?”. Not only did this show that the students were becoming lazy about their calculations, but it also supported the idea that the understanding wasn’t there. If they couldn’t convert, say, speed=distance/time into a triangle, then maybe they don’t understand the formula properly.

The triangles might be useful as scaffolding for low-attainers but it’s more beneficial to teach the understanding behind rearranging formula overall I think.

Then, on the 12th March 2021, I saw another formula triangle-based tweet.

Now, to be fair, I did laugh. It is pretty funny. If you read the whole thread, there are some more absolute gems there, and I’m still laughing. More seriously though, it completely reaffirms that the formula triangles become pretty much useless the second that there are either a) more than three variables, or b) there is an operation in the formula that isn’t multiply or divide.

Maybe my response to the tweet was a bit dramatic, but to be fair, I do hate it.